What SPC Is For

Statistical process control distinguishes two kinds of variation. Common cause variation is the natural spread of a stable process; special cause variation comes from something that changed. The purpose of a control chart is to tell them apart quickly, so that the process is adjusted when something changed and left alone when nothing did.

Variables and Attributes

Molding and stamping produce both kinds of data. Variables data, such as tooth pitch in millimetres or tape thickness in microns, carries more information per sample and is preferred wherever a gauge can produce a number. Attributes data, such as pass or fail on slider function, is used where measurement is impractical or where the characteristic is genuinely binary.

Use variables charts for dimensions and force, and attribute charts for function and appearance.

The Xbar-R Chart

The standard pair for a measured characteristic is the average and range chart. Take subgroups of four or five consecutive pieces at a fixed interval, calculate the average and the range of each subgroup, and plot both.

The control limits are built from the average of the subgroup ranges. For the averages chart, the upper limit equals the grand average plus a constant A2 multiplied by the average range, and the lower limit equals the grand average minus the same product. For the range chart, the upper limit equals a constant D4 multiplied by the average range, and the lower limit equals D3 multiplied by the average range. The constants depend only on subgroup size and are tabulated in every SPC reference.

Plot the range chart first. Averages hide spread, and an out-of-control range indicates a change in variability that makes the limits on the averages chart invalid. Reading the average chart while the range chart is out of control is one of the most common technical errors in shop-floor SPC.

The p Chart for Defectives

When the characteristic is pass or fail and the sample size varies, the p chart is appropriate. The centre line is the average proportion defective. The control limits are that proportion plus or minus three times the square root of the proportion multiplied by one minus the proportion, divided by the sample size.

Two practical cautions apply. When the sample size changes, the limits change with it, which is correct but visually confusing; plot the limits alongside the points. And when the average proportion is very small, the normal approximation behind the formula weakens, so a chart with an average below about one percent defective in samples of fifty should be replaced by a chart designed for rare events or by a longer period between samples.

Capability Indices

Control limits describe the process; specification limits describe the customer. Capability indices compare the two. The capability index Cp is the specification width divided by six standard deviations. The capability index Cpk is the smaller of two distances: the upper specification limit minus the mean, or the mean minus the lower specification limit, each divided by three standard deviations.

Cp measures potential and Cpk measures actual, because it accounts for centring. A process with a large Cp and a small Cpk is capable but off-target, which is usually a setup problem rather than a spread problem. Report Cpk for characteristics that matter, and report it with the sample period and the number of subgroups, because a capability index computed from too little data is a random number with a decimal point.

Applying It to Molding

Molding has a specific difficulty: consecutive pieces from the same shot are more alike than pieces from different shots, because they share cavity, material and thermal conditions. Subgroups of consecutive pieces therefore underestimate the true variation. Form subgroups across shots, one piece per cavity where possible, so that the chart reflects the variation the customer will experience.

The characteristics worth charting in a zipper plant are tooth pitch, body width, and a functional dimension such as slider channel height. Tool wear produces a slow trend rather than a jump, so trend rules matter more than the single-point rule.

Applying It to Stamping

Stamping is dominated by tool wear, which produces a gradual change in burr height, width and thickness. A chart that only reacts to points beyond the limits will run a worn tool until it produces defects, because wear arrives as a trend that stays inside the limits until it does not.

Two practices help. First, use trend rules in addition to the limit rule, so that six or seven consecutive points moving in one direction trigger attention. Second, record cumulative strokes since the last tool service and treat that counter as a second chart, because the counter is a leading indicator and the dimension is a lagging one.

Reaction Rules

A control chart without a reaction plan is a decoration. The plan should state, for each signal, who does what and how quickly. A workable structure distinguishes three levels:

  1. Out of control on the range chart: stop, check the setup and the material lot, quarantine output back to the last confirmed good subgroup.
  2. Out of control on the averages chart: check the adjustment, verify with a confirmatory sample, and record the action taken.
  3. Trend or run rule triggered but inside the limits: increase sampling frequency, inspect the tool or bath, and prepare a change before the limit is reached.

Recording the adjustment is as important as making it. Without a record, the same adjustment is made repeatedly and the chart shows a sawtooth that nobody can explain.

Preconditions

SPC rests on two assumptions that are often false. The first is a capable measurement system: a gauge study should show repeatability and reproducibility small relative to the tolerance, with ten percent commonly treated as good and thirty percent as the point at which the measurement system needs attention. The second is a stable process: a chart built during a ramp-up, a trial run or immediately after a tool change describes a process that does not yet exist.

YCC charts molding dimensions by cavity rather than by machine, because a single worn cavity disappears inside a machine-level average until it is producing scrap on its own. The chart is reviewed at the start of the shift, and the tool change decision is made from the trend rather than from the rejection.